A Novel Computational Model of the Dynamic Response of the Evaporating Liquid-Vapor Interface in a Capillary Channel

Abstract

A computational model is developed to investigate the dynamic response of an evaporating meniscus during the capillary flow between vertical parallel plates. A previously developed arbitrary Lagrangian-Eulerian (ALE) model was extended to directly track the formation and evolution of the evaporating meniscus during spontaneous liquid penetration within a capillary channel. The two-dimensional time-dependent conservation equations for mass, momentum, and energy were solved in a finite-volume framework implemented on a moving and deforming grid. The sharp interface tracking method developed here enables direct access to the flow variables and transport fluxes at the meniscus with no need for averaging techniques. The model was validated by comparing the predicted dynamic response of the capillary height subject to interfacial evaporation against theoretical results. The effects of wall spacing and liquid superheat on the capillary flow and the evaporation rate were studied. It was found that thermal diffusion adjacent to the meniscus has a critical effect on the evaporation rate, and neglecting it leads to significant overprediction of the evaporation rate. Results show that, in general, inclusion of evaporation causes a reduction of the liquid column height compared to the non-evaporating case. It was also observed that the equilibrium capillary height is inversely proportional to the liquid superheat. Analyses of the transient regime show that evaporation tends to dampen the oscillatory flow regime compared to the non-evaporating meniscus case.